We shall now present the operator topology used along this section. In particular, we deal with the Toeplitz in time operator class. These notions are based on the one introduced in [1]}, [2]}, [3]}, [4]}. We consider parameter dependent operators in the form
\(T:\mu \in \mathcal {O}\mapsto T(\mu )\in \mathcal {L}(H^s({d+1},\mathbb {C}))\) 
